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studies of Mental Fatigue 



In Relation to the Daily School Program 



W^. H. HECK, M. A. 

PROFESSOR OF EDUCATION, UNIVERSITY OF VIRGINIA 

AUTHOR OF 
"MENTAL DISCIPLINE AND EDUCATIONAL VALUES" 



SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN COLUMBIA UNIVERSITY 



LYNCHBURG, VIRGINIA 

J. P. BELL COMPANY, INCORPORATED, PRINTERS 

19 14 



0-^^ 



V 



V^^ 



TABLE OF CONTENTS 



PAGE 

Introduction 3 

First Study 5 

Conditions 5 

Material 6 

Method 10 

Grading 15 

Eesulf^ 17 

Second Study 27 

Third StUdy 33 

Conclusions 37 



dOK a 1314 



STUDIES OF MENTAL FATIGUE 



INTRODUCTION 

American books on school management and hygiene^ show a 
practical though not complete agreement as to the curves of 
fatigue in relation to the daily school program. Conclusions 
from German experiments on fatigue are the main bases for 
this American opinion, which is somewhat as follows: The 
child's efficiency, on the average, is greatest from about 9 :30 
(after a period for settling down to work) to 11 a. m., and then 
declines until the noon intermission ; the child comes back in 
the afternoon j^artially refreshed by the long recess and the mid- 
day meal, depending of course upon the length of the recess 
(usually one hour) and the quantity and quality of the food 
eaten ; the second high plateau of efficiency, which is lower than 
the corresponding plateau of the morning session, extends from 
about 1 :30 to 2 :30 p. m., and is followed by a decline to the 
lowest point of the day at the time of dismissal. Some writers 
believe that the second plateau occurs later in the afternoon 
than 1 :30 p. m. In a one-session school day the decline from 
the high morning plateau is interrupted to only a small degree 
by one or two short recesses, and extends to a point below that 
at the close of the morning session of a two-session day. 

Such text-book opinions are fast becoming guides for making 
daily school programs throughout the United States. Univer- 
sity departments of education, normal schools, summer schools, 
and teachers' reading circles are also urging reform in programs 
according to the following suggestions : The most difficult sub- 
jects in the curriculum, if they can be determined for a particu- 
lar class, should be placed, both for class recitation and for 
individual study, at the periods of greatest efficiency, with 
special emphasis upon the high morning plateau for arithmetic 

^For example: Arnold, School and Class Management, Vol. II, p. 33; 
Bagley, Educative Process, pp. 340-2, and Classroom Management, p. 57; 
Bolton, Principles of Education, pp. 274-5; Chancellor, Class Teaching and 
Manager.ient, pp. 122, 3; Colgrove, The Teacher and the School, p. 180; 
Cornell, Health and Medical Inspection of School Children, p. 193 ; 
Hollister, High School Administration, p. 254; O'Shea, Dynamic Factors 
in Education, pp. 286-290; Perry, Management of a City School, pp. 99, 
100; Roark, Economy in Education, pp. 65, 94; Seeley, New School 
Management, p. 49; Shaw, School Hygiene, pp. 230, 1. 



4 Studies of Mental Fatigue 

or language drill ; the less difficult subjects should be distributed 
appropriately along the curves of fatigue; and recesses, relaxa- 
tion exercises, and alternations of recitation with study periods 
should be used to defer and lessen the decrease in efficiency. 
Thus the waste of the child's energy would be checked and more 
school work be accomplished in a given time. 

The purpose of this monograph is not to review the vast and 
bewildering literature on fatigue, or even that which has domi- 
nated American thought on the daily school program, but to re- 
port experiments testing the validity of the prevailing American 
opinion and the suggestions based thereon.^ 



'I am greatly indebted to Dr. Edward L. Thorndike, Teachers' College, 
Columbia University, for many suggestions regarding this work. The sum- 
maries of experiments on Fatigue in iiis Educational Psychology, vol. iii, 
and in Offner's Menial Fafiguc (English translation by Whipple) render 
unnecessary any bil)Iiographical discussion in this monograph. My second 
and third experimetits were reported in the Psychological Clinic and the 
Journal of Educational Psychology. 



1 



FIRST STUDY 

CONDITIONS. 

The tests were given during the session 1911-12 to forty 
classes, 1,153 children, in four New York City schools, repre- 
senting different nationalities and different grades of social and 
hygienic opportunities. On four days (each being four or five 
days apart) in December, 1911, four classes of fifth-grade girls, 
mainly Russian Jews, were tested in Public School 177 ; on 
four Fridays in January, 1912, eight classes of 5 A boys, and on 
four Mondays eight classes of 5B boys, mainly Italians and Pol- 
ish Jews, were tested in Public School 83 ; on four Wednesdays 
in January four fourth-grade and four fifth-grade boys and 
girls, mainly Irish, German, and American, were tested in Pub- 
lic School 27; on two Wednesdays in March and two in April 
six fifth-grade and six sixth-grade boys and girls, mainly Ameri- 
can (with several negroes), were tested in Public School 3, 
Brooklyn. Fifteen of the forty classes tested were 5A classes 
and fifteen were 5B classes. Together they furnished the stand- 
ard for the work, but two 4A, two 4B, three 6A, and three 6B 
classes were chosen to represent other stages of advancement. 
The normal-aged and over-aged (E) sections of the half-grades 
in P. S. 177 and the high (a), middle (b), and low (c) sections 
of the half-grades in P. S. 3 were included, as were also the un- 
differentiated sections in P. S. 83 and 27. Of course the differ- 
ent ability of classes of different stages of advancement did not 
affect my results, because in any comparison of the work at the 
four periods of the school day the work of the same class would 
be represented at each period, and thus would be compared with 
itself and not with a less or more advanced class. The tests in 
P. S. 177, 83, and 27 came before the mid-session promotion; 
those in P. S. 3 came after, and therefore were given to some- 
what younger and less advanced children according to grade. 
Though more boys than girls took all four of the tests, the re- 
sults fairly represent both sexes. The December, March, and 
April tests were given in mild weather, the January tests in 
cold weather; and the ventilation of the classrooms was corre- 
spondingly varied, especially by the use of window ventilation. 
The ventilating and lighting systems were excellent in P. S. 
27, good in P. S. 177, and fair in P. S. 83 and 3. Twenty 
classes were tested on Wednesdays, eight on Fridays, eight on 
Mondays, and four on different days in the week, thus repre- 
senting supposedly varied -degrees of freshness in children in 
relation to the week's schooling. The children tested were 



6 Studies of Mental Fatigue 

under medical supervision and their most obvious physical 
defects, especially of a contagious kind, had been looked after; 
but very iew children had been given a general routine exam- 
ination by the school doctors. The daily school programs were 
not uniform, sometimes even in the same school, but showed a 
general tendency to give arithmetic in the early morning. In 
P. S. 83 a group system was used throughout^ about half of a 
class being grouped around the teacher for study while the 
other half carried out previous directions as to work at black- 
boards or desks. 

The differences as to social and hygienic condition of children 
and schools, and as to months and days, did not affect my com- 
parisons of the work of the classes at four periods of the school 
day, because the classes were tested and compared in groups 
of four, every class in a gi'oup having almost the same conditions 
and being tested on the same days. These variations in the 
groups as a whole were purposely sought to see if any conse- 
quent changes could be noticed in the work of the groups as com- 
pared with each other, but they were so slight as to be negligible. 
The differences in children and schools were representative 
of New York City school conditions, though the four schools 
selected were superior in supervision. 

MATERIAL. 

As my aim was to find out what decrease in efficiency re- 
sulted from the progTess of the day and especially of the school 
work, I determined to test a large number of children at four 
different periods of the school day and compare the quantity 
and the quality of the work done. Not the slightest change 
was to be made in the ordinary school routine except the in- 
terruptions for the short time necessary to give the tests. My 
desire was to select test material as nearly like the actual lessons 
of the children as possible and thus avoid the artificiality, at 
least for my purpose, of most of the physiological and psycho- 
logical tests so far made. I therefore chose, as most suitable 
for my purpose, the four fundamental operations of addition, 
subtraction, multiplication, and division with whole numbers. 
Of course these operations could not represent all of arithmetic 
or all of the curriculum, but neither could any other test 
material; and as the basis of all number work they were as 
representative as any part of the elementary curriculum 
could be. 

In order to carry out my plan of testing children at four 
periods of the school day, and comparing the work done, I had 



Material 7 

to have four different tests so similar in quantity and quality 
that a certain proportion of correct and incorrect work in the 
first test would be as nearly equal as possible to the same pro- 
portion in any one of the other three tests. Only in this way 
could the work at the four periods be conveniently compared. 
Of course it was impossible to have four different tests exactly 
equal as to quantity and quality, but the reader can see from 
the third and fourth tests herein printed that this result was 
very nearly approached. 

As the Standard Tests in Arithmetic, by Mr. S. A. Courtis 
of Detroit, are widely recognized as well planned and graded, 
I obtained Mr. Courtis' kind permission to modify and use 
his Test No. 7, and also his imitation of it, which differed 
almost entirely by a shifting of the figures in each example. 
With my first and second tests thus furnished, I made out the 
third and fourth in imitation of these by a similar shifting of 
the figures. In the few examples where a figure was substituted 
by Mr. Courtis in the second test for one in the first, that 
figure reappeared in the fourth test but not in the third. Mr. 
Courtis' tests were not entirely suitable for my purpose in three 
particulars: (1) The required transfer by the child of the 
examples and of the answers could not be reduced to a propor- 
tionate measurement along with the work in the operations 
themselves. Consequently each example in my tests was 
printed in workable form with space underneath for the figures 
to be made by the child. (2) The arithmetical symbols were 
eliminated, and the operations necessary were designated by 
the words, ^'Add," etc., above the examples. (3) Example 
la, 2a, 9, and 17 were omitted, thus making each test consist 
of three examples each in addition, subtraction, multiplication, 
and division. The examples were printed in three parallel 
rows, each row with one example in each operation in the order 
just given. (These modifications were made by me without 
consulting Mr. Courtis, and he is in no way responsible for 
them.) The first row contained examples with no, the second 
with simple, and the third with advanced, borrowing and carry- 
ing. However advantageous it might have seemed for all the 
examples to have been of approximately equal difficulty, the 
wisdom of Mr. Courtis' three grades of difficulty was shown 
in the zest gained by the children in my tests from the rapid 
start with the easy examples of the first row. (The third and 
fourth tests are herewith given, the original size — 8^ x 11 
inches — and type being reduced.) 











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10 Studies of Mental Fatigue 

METHOD. 

I explained to the teachers beforehand the purpose and 
method of my experiments and asked them to remain in the 
room while the tests were being given. They were earnestly 
requested not to take any part in explaining or directing the 
work, not to discuss the tests with the children at other times, 
and not to vary the prescribed arithmetic lessons in the slightest 
so as to stress the four fundamental operations. (The children 
were doing more advanced work.) As far as I know, these 
requests were faithfully carried out, and the teachers were 
always courteous in making way for my work. I eliminated 
the teachers from any part in conducting the tests, because 
uniformity in method was possible only with one conductor 
throughout. 

The presence of the teacher in a classroom gave the customary 
organization as a background for my tests. The method of 
presenting the tests to the children was worked out with great 
care. When I entered a classroom for the first time, the teacher 
directed the children to put aside whatever work they were 
doing individually or collectively. I then explained the nature 
of my four tests, the order in which the examples were to be 
done (with a caution not to skip the examples in division), and 
the directions for starting and stopping work immediately on 
signal. These explanations were almost the same to all classes 
and seemed so clear that most of the children began the first 
test with nearly as much understanding as they did the other 
three. An inevitable initial interest partly balanced whatever 
initial disadvantage the children may have had in the first test. 
The introductions to the later tests were very brief. The 
children thought they were being examined for correctness in 
speed and never realized the main purpose of the tests. More- 
over, they did not know that their results would have no effect 
upon their school standing. 

When all pencils were ready (in P. S. 83 pens were used) 
the teacher and I put on each desk one test sheet with the back 
side up. The children were not allowed to touch the tests until 
told to write on the back of the sheets the number of the school, 
the date, and the name, age, and class of pupil. (Later on I 
inserted the time of day when the test began.) On signal, the 
children turned the papers over immediately and began to work 
the examples in the numbered order. They worked steadily as 
directed, with surprisingly little hurry or interruption, until 



Method 11 

told to stop, when they turned their papers over without put- 
ting down another figure. During the test, I quietly watched 
the children and their papers, so as to prevent cheating, toward 
which there was little inclination, and to see that the examples 
were worked in proper order and without hurry, especially 
toward the end. The children did not know how much time 
was being allowed, the progress of time was not mentioned, and 
I consulted my watch almost without being noticed. 

The time limit for each test was ten minutes, not long enough 
for the children to be fatigued by the test itself. Great care 
was taken to be exact in starting and stopping. The first four 
(those in P. S. 177) of the forty classes tested were given 
twelve minutes, which time, of course, was maintained through- 
out the four tests with these classes, and did not affect the total 
results as far as my purpose was concerned — the twelve-minute 
tests being compared only with each other. But as many 
children in these four classes finished in ten or eleven minutes, 
the time limit was reduced to ten with the other classes. Even 
then several children finished a little before ten minutes and 
generally spent the extra time in looking over and correcting 
their work. 

Those children that finished early put themselves at a 
possible disadvantage, if, in their speed, they sacrificed quality 
to quantity and were unable to increase the quantity further 
by working extra examples up to the full time allowed. How- 
ever, as the total tests showed slightly more work and a slightly 
greater per cent of error at the periods after the first period, 
these disadvantages might have had slightly more influence 
and been added to the fatigue effect at those periods. That 
this difference is small is shown by the fact that the five groups 
which included far more than half of the completed tests had, 
as averages for the five groups and for the three periods, a 
smaller increase in amount of 0.47 per cent, and only a greater 
decrease in correct work of 0.04 per cent than did all the ten 
groups combined into one total group. If any possible dis- 
advantage affected the results of these five groups, it was 
swallowed up in their superior ability. In a note on page 21 
are given the comparisons of the four periods, after the results 
of the twelve-minute tests in P. S. 177, which many children 
finished, were subtracted from the total group with its similar 
comparisons. The comparisons, before and after this subtrac* 
tion, are so nearly alike and the slight differences are so con- 



12 Studies of Mental Fatigue 

flicting, as signs of fatigue, that it matters little whether the 
differences be attributed to early finishing or to chance varia- 
tion in P. S. 177. Whatever small effect early finishing in 
the ten groups tested may have had upon my results, this effect 
would strengthen my conclusions as to the little fatigue shown 
in my tests, because the subtraction of it from the fatigue 
effect would lessen, of course, the signs of fatigue just to that 
degree. In fact, I might emphasize the advantage to my con- 
clusions of the possible disadvantage of early finishing. 

The children seemed to enjoy the tests. I was surprised at 
my success in keeping their interest nearly the same at all four 
periods of the school day, so that their zeal in the work would 
be as constant as possible and not in favor of any period. In 
this way there was eliminated almost entirely the element of 
boredom — probably the greatest influence in decreasing the 
quantity and quality of work in the ordinary routine of the 
school day. Studies of mental fatigue should be well guarded 
against the interference by boredom, which is often confused 
with fatigue, and which has vitiated the results of several ex- 
periments. This confusion is general in teachers' estimates 
of fatigue and renders them of little value for scientific study. 

The time schedule^ was arranged so as to test the children at 
approximately 9:10 a. m., 11:05 a. m., 1:10 p. m., and 2:30 
p. M. — near the opening (after a brief period for settling down 
to work) and the close of the morning and afternoon sessions. 
The exact time varied from these points according to the number 
of classes to be tested in a day, the time of my arrival in a 
classroom, and the length of preparation necessary. The classes 
in the different schools were combined into groups of four, 
either one, two, or three groups being tested in a day. With 
only one group in P. S. 177" the above schedule could be closely 
adhered to; but with two groups a day in P. S. 27 and 83, and 
three groups in P. S. 3, two classes and three classes, re- 
spectively — one from each group — were tested in immediate 
succession at each of the four periods of the school day. 
The classes of the second group followed the corresponding 
classes of the first group just as soon as I could get from the 



'In most classes there were two-minute formal gymnastic drills at eleven 
and two o'clock. I was unable to detect any effect of these drills toward 
increasing or decreasing fatigue; but the eleven o'clock drill may have 
benefited the work at the second period to a slight degree. 

In this school an extra class was tested at an odd period but had no 
place in my experiment. 



Method 



13 



one classroom to the other and start the test with the later class. 
In P. S. 3 the classes of the third group followed those of the 
second group in a similar time relationship. With two or 
three groups to be tested, the fourth period was begun before 
2.30 p. M. so that the work could be completed before the 
3 :00 p. M. dismissal. The following time schedule is typical : 





Time Schedule — Public School 83 — 5B Classes. 


Group 


Class 


First Test 


Second Test 


Third Test 


Fourth Test 






Jan. 8 


Jan. 15 


Jan. 22 


Jan. 29 


1 


5B1 


9:12 


11: or, 


1:04 


2:24 


2 


5B2 


9:341/2 


11:221/2 


1:20 


2:39 


1 


5B3 


11:04 


1:041/2 


2:23 


9:111/2 


2 


5B4 


11:231/2 


1:20 


2:381/2 


9:261/2 


1 


5B5 


1:081/2 


2:25 


9:051/2 


11:041/2 


2 


5B6 


1:29 


2:41 


9:22 


11:22 


1 


5B7 


2:231/2 


9:081/2 


11:05 


1:081/2 


2 


5B8 


2:441/2 


9:26 


11:21 


1:25 



It is evident that the time relationship of the classes 
of the first group to each other was almost the same as 
that of the classes of the second, or of the third, group to 
each other. The results for my purpose were not affected by 
thus testing the classes of one group after the corresponding 
classes of a preceding group, because each group constituted a 
unit by itself for my comparison of the four periods of the 
school day. In fact, the advantage of a wider representation 
of the morning and afternoon sessions was thereby gained. For 
instance, the tests with the first groups about 9:10 a. m., which 
might possibly have come in a few classes before the children 
had settled down, were balanced in the total results by the tests 
with the second groups about 9 :27 a. m. However, a compari- 
son of the fatigue shown by these groups gives no preference 
to either time for the first period. 

The most important features of the time schedule were the 
balancing and consequent neutralization of the practice effect 
in the second, third, and fourth tests. Thereby the fatigue 
effect was left free for my comparison of the quantity and 
quality of the work at the four periods. This was done by 
having each of the four tests taken at each of the four periods 
by one of the four classes in a group. The first test was taken 
at the first period by the first class, at the second period by the 
second class, at the third period by the third class, and at the 



14 Studies of Mental Fatigue 

fourth period by the fourth class; the second test was taken 
at the first period by the fourth class, at the second period by 
the first class, at the third period by the second class, and at the 
fourth period by the third class ; the third test was taken at 
the first period by the third class, at the second period by the 
fourth class, at the third period by the first class, and at the 
fourth period by the second class ; the fourth test was taken at 
the first period by the second class, at the second period by 
the third class, at the third period by the fourth class, and at 
the fourth period by the first class. With two groups to be 
tested in one day, the four classes in the second group followed 
the above schedule about seventeen minutes after the correspond- 
ing classes of the first group. In P. S. 3 the third group fol- 
lowed the second group in similar order. By such a schedule the 
work of the group at each period included all four tests (each 
test was generally taken a week apart), and consequently the 
practice effect of one class at the second period, of another class 
at the third period, and of another class at the fourth period. 

This arrangement was based on the belief that, if each test 
were taken by each class at the same period, the practice effect 
of any one class in the second, third, or fourth test would be 
almost equal to the practice effect of any other class in its 
group in the corresponding test ; and that, as each period in- 
cluded the practice effects in the second, third, and fourth tests, 
the sum of the three practice effects of a group at any one 
period would be balanced and neutralized by the sum of the 
three almost equal practice effects of the same group at any 
other period. This belief in the approximate equality of the 
practice effect of the four classes in a group can not be proved 
or disproved by my results, because the same test was taken 
at different periods by the four classes, and the practice effect 
of any class was thereby complicated with a different fatigue 
effect and rendered incomparable with the practice effect of 
any other class in its group in the same test. If there were 
differences in the practice effect of the four classes in a group, 
especially of those classes at different stages of advancement, 
they were probably very slight. Even these differences were 
partially neutralized in my total results, since the classes in 
different groups were not tested in the same order of advance- 
ment: in P. S. 177 in ascending order, in P. S. 83 on the 
same level of advancement, in P. S. 27 in descending order, 
and in P. S. 3 in ascending order. (As the four half-grades in 
P. S. 3 were divided into a, b, and c sections according to 



Grading 15 

ability, these sections were combined into a, b, and c groups; 
and the results show some positive though not consistent corre- 
lation between ability and resistance to fatigue.) This varia- 
tion gave a different relationship between practice and fatigue 
effects in the different groups according to the periods at which 
the corresponding tests were taken by the more advanced and 
by the less advanced classes. 

The figiTres on page 26 show that the practice effect in the 
forty classes tested was small, especially because (1) an initial 
interest partly balanced whatever initial disadvantage the 
children may have had in the first test, (2) the work was rapid 
and short, (3) a week generally intervened between the tests, 
and (4) no class drill on the subject-matter of the tests was 
allowed. However, the elimination of the practice effect from 
my results frees this experiment from the error common to 
most of the experiments on mental fatigue in relation to the 
daily school program. 

The practice effect within a single test was not considered. 
With tests having simple examples of the same kind, such a 
result were possible ; but with the variety of examples in my 
tests, both in kind and in difficulty, the accumulation of a 
practice effect during the ten minutes could hardly have taken 
place. Even if there were such practice effect in my results, it 
would have been balanced against itself in my comparison of 
the four tests at the four periods. 

GEADING. 

The papers were filed and graded, and the results tabulated, 
according to school, test, class, and name. Only full sets of 
four tests per child were used, all partial sets being thrown out. 
Unless called back to their former class for my work, the 
children who were removed to another class, after one or more 
tests, took the remaining tests at wrong periods, thus causing 
all their papers to be thrown out. In spite of many absences 
and removals, 1,153 children in the forty classes worked the 
four tests in proper order. 

The grading of the 4,612 papers necessitated such tedious 
and conscientious attention to details, that it was not "farmed 
out" to others, who might have been careless, but was done 
entirely by my wife and me. The care taken to be exact and 
to go over the papers again in search for possible errors in 
grading extended the time for this work to four months. In 



16 Studies of Mental Fatigue 

the detailed method used, every figure the child put do\vn in 
working the examples was graded right or wrong, a complete 
paper in each test including 190 figures. No child was given 
a total credit of right or wrong figures for an example or part 
of an example greater than that necessary for the correct work- 
ing of that example or that part, though the mistake of a child 
would often involve a gi'eater number of figures. On the other 
hand, the completion of work on an example or part of an 
example gave the child the total credit of right or wrong 
figures for that example or that part, whether the child had 
put down that number of figures or not. Misplaced figures 
were counted wrong, as were also the omitted figures in those 
examples that had been "worked by the child. In addition to 
these main rules for grading the papers, there were many sub- 
sidiary and consistent rules for special cases, which helped 
greatly in threading the jungle of right and wrong figures 
which a child would sometimes create. 

Every method of grading arithmetic papers is open to objec- 
tions, but, for my exact comparison of the work at four periods 
of the school day, the detailed method used seemed far prefer- 
able. Most of the objections which might be urged against 
this method would not apply to the present case, as the aim 
was not to give an absolute grading of ability in the four 
fundamental operations, but simply to be consistent in judging 
the quantity and quality of the work at the four periods. It 
might be urged that the value of the figures in some examples 
or parts of examples was not equal to that of those in other 
examples or parts of examples. But where a child worked the 
similar examples in all four tests the method of marking was 
the same for all tests, and therefore for all periods. It is only 
where a child worked one or more examples in one or more 
tests, but not the similar examples in the other tests, and where 
tli;^ figures in these particular examples could be shown to-be 
U)i '( rvalued in comparison with the figures in those examples 
tl::;r had been worked in all four tests, that the above-mentioned 
objection has any validity. The valuation of the figures in the 
ninth example in comparison with that of those in the fifth, 
in the few cases where the ninth example was worked by a 
child in some tests but not in others, is the only illustration 
that might possibly afl:'ect my results to more than a negligible 
degree. Whatever small effect a possible disparity in the value 
of figures in these and other examples might have had upon 
my results would strengthen my conclusions as to the little 



Results lY 

fatigue shown in my tests, because the subtraction of this effect 
from the fatigue effect would lessen, of course, the signs of 
fatigue just to that degree. In fact, I might emphasize the 
advantage to my conclusions of this possible disparity. 

Another objection may be made that an initial wrong figure 
may involve a series of figures which, though wrong, are really 
the correct consequence of the first mistake and that, therefore, 
only the initial figure should be counted wrong. To trace out 
from every initial wrong figure in every example in 4,612 
papers all the consequent figures, and to determine whether 
the latter figures were correct consequences of the former, would 
be an interminable task. Even then there would never be cer- 
tainty that the consequent figures, in individual papers, did not 
include more initial wrong figures than the first one. As the 
necessary thing in my experiment was to grade consistently the 
work at all four periods, and, as every figure was graded accord- 
ing to the same rules for these periods, the change suggested, 
even if possible, would not have affected my results. 

In order to strengthen my comparison of the work at the 
four periods by using two different methods of grading, rather 
than one alone, all the papers were graded again by a gross 
method in which only the answers were considered. The gross 
method chosen was very similar to that used by Mr. Courtis. 
The first and second examples were together credited with one 
point, this point being counted wrong on account of one or 
more mistakes in either example ; the third, fourth, fifth, sixth, 
and tenth examples were each credited with one point, the 
point for a given example being counted wrong on account of 
one or more mistakes in that example ; the seventh, eighth, 
ninth, eleventh, and twelfth examples were each credited with 
two points, one point for a given example being counted wrong 
on account of one mistake, and two points being counted wrong 
on account of two or more mistakes in that example. 

RESULTS. 

After the results for each child were graded by the detailed 
method and tabulated, the number of right and wrong figures 
for each class in each test was averaged, and. then the number 
of right and wrong figures for each group of four classes at 
each of the four periods of the school day. The individual 
variations in the children were first merged in the class aver- 



18 



Studies of Mental Fatigue 



ages and again in the group averages. From these averages 
were made tables for each of the ten groups. The following 
table is typical: 

Table of Results — Group 2 — Puhlic School 27. 



5B1 
5A1 
4B2 
4A2 
4 



26 
43 
32 
26 
127 



FIRST PERIOD 



Test Right Wrong 



129.69 
149.07 
131.53 
112.08 



14.92 
15.98 
17.53 
20.65 



130.59 17.27 



SECOND PERIOD 



THIRD PERIOD 



Test Right IWrong Test Right Wrong 



132.35 
126.98 
122.72 



25.31 
12.12 
24.84 



126.69 24.69 
127.18 21.74 



142.77 
142.16 
109.56 
122.96 
129.36 



FOURTH PERIOD 



23.42 

21.44 
22.25 
28.35 
23.86 



Test Right Wrong 



140. 3r 25.27 
145.28 20.21 
124.50 20.47 
101.88 23.58 
127.99 22.38 



Sum of right and 

wrong 147.86 

Relative amount done 100.00 

Per cent right 88.32 

Relative per cent 
right 100.00 



148.92 

100.72 

85.40 

96.69 



153.22 

103.63 

84.43 

95.64 



150.37 

101.70 

85.12 

96.38 



These tables gave answers to two questions, which formed 
the core of the investigation. The answer to first question, 
What was the difference in the quantity of work done at the 
four periods ?, was reached by getting the sum of right and 
wrong figures at each period, by giving the value of 100.00 to 
the sum at the first period (of course any other period could 
have been taken as the standard of comparison), and then by 
calculating the per cents of this sum represented by the sum at 
each of the other three periods. These per cents for the ten 
groups were as follows, the per cent for the first period being 
100.00 in every group : 



Group 


School 


Second Period 


Third Period 


Fourth Period 


1 


177 


103.16 


101.36 


103.19 


2 


27 


100.72 


103.63 


101.70 


3 


27 


100.14 


98.28 


96.62 


4 


83 


100.49 


100.37 


105.81 


5 


83 


98.85 


98.60 


104.05 


6 


83 


102.42 


101.65 


103.52 


7 


83 


102.15 


102.17 


101.87 


8 


3 


101.41 


101.20 


103.74 


9 


3 


101.05 


104.40 


99.99 


10 


3 


104.34 


104.26 


104.54 



Results 



19 



The answer to the second question, What was the difference 
in the quality of work done at the four periods?, was reached 
by calculating the per cent right of the sum of right and wrong 
figures at each period, by giving the value of 100.00 to the 
per cent right at the first period, and then by calculating the 
per cent of this per cent right represented by the per cent at 
each of the other three periods. These per cents for the ten 
groups were as follows, the per cent for the first period being 
100.00 in every case : 



Group 


School 


Second Period 


Third Period 


Fourth Period 


1 


177 


97.53 


97.58 


97.37 


2 


27 


96.69 


95.64 


96.38 


3 


27 


98.86 


97.34 


97.54 


4 


83 


100.39 


98.65 


97.94 


5 


83 


98.92 


96.90 


95.89 


6 


83 


97.64 


100.94 


98.65 


7 


83 


97.81 


99.12 


98.91 


8 


3 


101.74 


101.39 


100.52 


9 


3 


98.75 


99.15 


97.45 


10 


3 


96.75 


99.06 


97.08 



In quantify of work done (sum of right and wrong figures) 
as compared with the first period, seven of the ten groups tested 
showed an increase at three periods, one an increase at two 
periods and a decrease at one period, and two an increase at 
one period and a decrease at two periods. In all, there were 
twenty-five cases of increase, averaging 2.53 per cent; and 
five cases of decrease, averaging 1.53 per cent. The same facts 
by periods were as follows : at the second period an average 
increase of 1.76 per cent in nine groups and a decrease of 1.15 
per cent in one; at the third period an average increase of 2.38 
per cent in eight groups and an average decrease of 1.56 per 
cent in two; at the fourth period an average increase of 3.55 
per cent in eight groups and an average decrease of 1.69 per 
cent in two. 

In quality of work done (per cent of sum right) as compared 
with the first period, seven of the ten groups tested showed a 
decrease at three periods, two a decrease at two periods and 
an increase at one period, and one an increase at all periods. 
In all, there were twenty-five cases of decrease, averaging 2.26 
per cent, and five cases of increase averaging 1.00 per cent. 
(The five cases of increase in quality occurred in different 
groups from those having the five cases of decrease in quantity ; 
consequently there was no connection between them.) The 



20 Studies of Mental Fatigue 

same facts by periods were as follows: At the second period 
an average decrease of 2.13 per cent in eight groups and an 
average increase of 1.06 per cent in two groups; at the third 
period an average decrease of 2.07 per cent in eight groups and 
an average increase of 1.16 per cent in two groups; at the 
fourth period an average decrease of 2.53 per cent in nine 
groups and an increase of 0.52 per cent in one group.^ 

The most important summary of results is shown in the total 
table combining the forty classes of the ten groups tested, in 
which individual, class, and group variations were all merged. 
The average of the forty class averages for each period was 
used as the material for calculating the comparative per cents 
of quantity and quality exactly in the same way that the aver- 
age of four class averages for each period was used in a table 
for each single group. ^ The balanced relation to each other 
of the four classes in each group was not disturbed by this com- 
bination, which tended, however, to neutralize whatever chance 
variations may have occurred in the single groups. In quantity 
of work done (sum of right and wrong figures) as compared 
with the first period of the school day, the ten groups together 
showed a respective increase of 1.57, 1.6U, and 2.36 per cent 
at the second, third, and fourth periods; and in quality of work 
done (per cent of sum right) a respective decrease of 1.51, l.Ul, 
and 2.22 per cent at the second, third, and fourth periods J For 
comparison with these results, obtained by the detailed method 
of grading, a similar total table luas made tvith the class aver- 
ages by the gross method of grading, and the following per 
cents were calculated : In quantity of work done (sum of right 
and wrong points) as compared with the first period, the ten 
groups together showed a respective increase of 1.92, 1.31, and 
2.27 at the second, third, and fourth periods; and in quality 
of ivork done (per cent of sum right) a respective decrease of 



^In order to give also the results bv schools, the first and second groups 
of P. S. 27, of P. S. 83-5 A, and of P. S. 83-5B, and the first, second, and' 
third groups of P. S. 3, were combined into four tables hx getting the 
group averages for eacli period of the eight or twelve class averages in the 
groups combined, and calculating therewith the comparative per cent of 
quantity and quality exactly in the same way as in the single groups. 

-The average of the forty class averages was used instead of the average 
of the ten group averages, as being more representative of the total con- 
ditions; but the diflference between the two total averages would be very 
small. 



Eesults 21 

5.7Ji, Jf.56j and 6. 66 at the second, third, and fourth periods.^ 
The per cents of increase in quantity in the two tables are sur- 
prisingly similar; the per cents of decrease in quality in the 
second table are a little over three times as large as those in 
the first table, but are still very small. This difference is 
probably due to the greater weight given errors by the gross 
method of grading, one error in the answer to any example 
making wrong one point out of a total of sixteen points for 
the entire test. This seems to me a defect natural to any gross 
method of grading for purposes of scientific study. (Notice 
the difference in the per cents of decrease in quality in the 
practice results on page 26.) However, it would be inevitable 
that any two, or any three, methods of grading would show 
some differences in results. The two total tables are given 
herewith. The one for the gross method of grading contains, 
of course, all the class averages necessary to make out the single 
table for each group ; but this extra work was not needed and 
therefore was not undertaken. 



^Subtracting the four classes of P. S. 177, as suggested on page 12, we 
have for thirty-six classes, by the detailed method of grading, an increase 
of 1.35, 1.68, and 2.24 per cent, respectively, in quantity, and a decrease 
of 1.39, 1.26, and 2.17 per cent, respectively, in quality; by the gross 
method of grading an increase of 1.70, 1.52, and 1.97 per cent, respectively, 
in quantitj', and a decrease of 6.31, 4.41, and 6.59 per cent, respectively, 
in quality. 



22 



Studies of Mental Fatigue 



Forty Classes (Ten Groups) Combined Into One Group. 
Detailed Method of Grading. 



g 


o 
o 

,c 


5 




FIRST PEKIOD 


SECOND PEBIOD 


THIRD PERIOD 


FOURTH PERIOD 


<s 


Test 


Right 


Wrong 


Test 


Right 


Wrong 


Test 


Right 


Wrong 


Test 


Right 


Wrong 


1 


177 


5A1 


29 


1 


150.34 


10.59 


2 


155.28 


23.17 


3 


162.07 


16.31 


4 


167.79 


19.14 


2 


27 


5B1 


26 


1 


129.27 


15.35 


2 


131.96 


25.31 


3 


142.77 


23.42 


4 


140.31 


25.27 


3 


27 


5B2 


25 


1 


135.80 


15.52 


2 


142.76 


26.56 


3 


144.36 


27.48 


4 


137.36 


28.56 


4 


83 


5A1 


35 


1 


99.09 


19.00 


2 


108.09 


16.94 


3 


113.26 


19.60 


4 


116.97 


28.86 


5 


83 


5A2 


37 


1 


92.22 


19.51 


2 


103.57 


19.19 


3 


109.16 


21.49 


4 


109.57 


27.24 


6 


83 


5B1 


36 


1 


100.47 


12.69 


2 


110.33 


16.72 


3 


123.42 


11.28 


4 


119.78 


17.19 


7 


83 


5B2 


32 


1 


114.12 


9.91 


2 


117.41 


19.91 


3 


126.06 


14.16 


4 


123.78 


15.06 


8 


35Aa 


28 


1 


110.11 


15.46 


2 


115.86 


17.54 


3 


125.14 


15.68 


4 


127.54 


18.18 


9 


3 5Ab 


19 


1 


109.89 


23.74 


2 


115.47 


23.32 


3 


130.37 


29.16 


4 


112.79 


30.76 


10 


3 


5Ac 


19 


1 


92.95 


14.05 


2 


96.42 


24.11 


3 


113.79 


21.89 


4 


101.47 


25.16 


1 


177 


5B1 


38 


4 


159.67 


11.34 




155.68 


12.42 


2 


158.53 


11.11 


3 


164.32 


10.53 


2 


27 


5A1 


43 


4 


148.81 


16.58 




126.93 


12.16 


2 


142.88 


21.70 


3 


144.88 


20.21 


3 


27 


5A2 


31 


4 


153.16 


17.71 


f 


138.13 


12.06 


2 


144.00 


21.00 


3 


151.84 


22.06 


4 


83 


5A3 


38 


4 


102.92 


20.89 


1 


92.63 


16.08 


2 


99.05 


18.79 


3 


112.92 


17.71 


5 


83 5A4 


26 


4 


110.46 


25.81 




87.62 


18.12 


2 


98.35 


25.81 


3 


111.19 


25.92 


6 


835B3 


28 


4 


111.86 


18.43 




100.32 


15.61 


2 


110.68 


15.50 


3 


112.43 


18.89 


7 


83 5B4 


27 


4 


114.78 


20.15 


1 


98.63 


18.30 


2 


113.07 


18.26 


3 


118.96 


21.00 


8 


35Ba 


29 


4 


132.14 


16.93 




126.17 


15.14 


2 


127.59 


20.66 


3 


133.07 


17.79 


9 


3i5Bb 


23 


4 


126.43 


24.43 




116.04 


25.96 


2 


122.30 


29.00 


3 


123.74 


23.26 


10 


35Bc 


15 


4 


106.67 


28.00 




106.13 


26.60 


2 


113.40 


28.87 


3 


111.20 


32.60 


1 


177 5Ea 


40 


3 


164.60 


8.92 


4 


158.17 


13.35 




136.35 


16.15 


2 


143.62 


16.07 


2 


27 


4B2 


32 


3 


131.66 


17.56 


4 


122.53 


24.84 




109.22 


22.56 


2 


123.87 


21.03 


3 


27 


4B3 


27 


3 


137.37 


22.85 


4 


130.33 


31.59 




113.37 


22.89 


2 


123.48 


25.15 


4 


83 


5A5 


40 


3 


107.42 


20.07 


4 


106.60 


24.40 




93.12 


18.00 


2 


105.47 


23.05 


5 


83 


5A6 


29 


3 


116.59 


13.14 


4 


117.41 


17.90 




90.14 


17.62 


2 


105.79 


19.01 


6 


83 


5B5 


25 


3 


110.60 


11.80 


4 


106.04 


20.60 




89.24 


11.04 


2 


107.00 


18.04 


7 


83 


5B6 


27 


3 


108.15 


20.26 


4 


108.63 


22.56 




95.04 


19.59 


2 


104.07 


21.44 


8 


3 


6Aa 


30 


3 


155.97 


14.47 


4 


156.93 


12.83 




151.90 


9.97 


2 


152.77 


18.20 


9 


3 


6Ab 


34 


3 


149.76 


15.68 


4 


143.68 


20.91 




136.03 


19.50 


2 


138.85 


21.91 


10 


3 


6Ac 


24 


3 


126.04 


21.50 


4 


120.29 


31.00 




112.21 


24.29 


2 


122.12 


25.54 


1 


177 


5Eb 


31 


2 


152.26 


13.71 


3 


161.61 


13.00 




163.10 


16.94 




154.16 


17.23 


2 


27 


4A2 


26 


2 


112.08 


20.65 


3 


126.65 


24.73 




122.96 


28.35 




101.88 


23.58 


3 


27 


4A3 


25 


2 


101.88 


31.96 


3 


114,12 


22.12 


4 


105.92 


27.60 




86.56 


20.48 


4 


835A7 


29 


2 


99.31 


14.17 


3 


105.00 


19.45 


4 


99.28 


23.55 




88.21 


17.72 


5 


83'5A8 


29 


2 


94.79 


11.86 


3 


96.28 


18.72 


4 


97.93 


17.07 




86.52 


18.72 


6 


835B7 


26 


2 


122.50 


16.73 


3 


128.77 


18.92 


4 


133.73 


18.50 




113.46 


16.46 


7 


83;5B8 


21 


2 


115.95 


16.86 


3 


127.95 


18.00 


4 


124.57 


20.71 




109.62 


15.95 


8 


36Ba 


28 


2 


140.07 


20.07 


3 


156.43 


12.86 


4 


147.64 


13.86 




147.89 


12.39 


9 


3 6Bb 


25 


2 


128.80 


17.36 


3 


138.64 


18.32 


4 


144.32 


11.68 




126.36 


18.40 


10 


3 6Be 


21 


2 


130.19 


21.71 


3 


137.38 


22.67 


4 


131.43 


18.24 




127.86 


19.71 




40 


1,153 




122.68 


17.69 




122.72 


19.85 




122.94 19.73 




122.79 


20.89 


Sum of 


right a 


nd 














wrong . . 




.. 140.37 




142.57 




142.67 




143.68 


Relative ai 


mount do 


ne 100.00 




101.57 




101.64 




102.36 


Per cent r 


ight 


.. 87.40 




86.08 




86.17 




85.46 


Relative pe 


r cent rig 


ht 100.00 




98.49 




98.59 




97.78 



Results 



28 



Forty Classes (Ten Groups) Combined Into One Group. 
Gross Method of Grading. 



a 

s 
o 


o 
o 

02 


3 


■ft 


FIKST PERIOD 


SECOND PERIOD 


THIRD PERIOD 


FOURTH PERIOD 


C5 


Test 


Right 


Wrong 


Test 


Right 


Wrong 


Test 


Right 


Wrong 


Test 


Right 


Wrong 


1 


177 


5A1 


29 


1 


11.38 


2.21 


2 


10.69 


3.90 


3 


11.28 


3.62 


4 


11.66 


3.79 


2 


27 


5B1 


26 


1 


9.23 


2.96 


2 


8.58 


4.35 


3 


9.27 


4.54 


4 


9.00 


4.65 


3 


27 


5B2 


25 


1 


9.40 


3.28 


2 


9.20 


5.00 


3 


8.92 


5.36 


4 


8.48 


5.20 


4 


83 


5A1 


35 


1 


6.14 


2.89 


2 


6.51 


3.80 


3 


6.91 


3.71 


4 


7.11 


4.66 


5 


83 


5A2 


37 


1 


6.03 


3.24 


2 


6.38 


3.43 


3 


6.46 


4.62 


4 


6.49 


4.84 


6 


83 


5B1 


36 


1 


6.56 


2.22 


2 


7.33 


2.75 


3 


8.44 


2.47 


4 


7.92 


3.33 


7 


83 


5B2 


32 


1 


7.28 


2.62 


2 


7.28 


4.16 


3 


8.62 


3.16 


4 


7.84 


3.87 


8 


3 


5Aa 


28 


1 


7.57 


2.50 


2 


7.21 


3.75 


3 


8.46 


3.25 


4 


7.89 


3.64 


9 


3 


5Ab 


19 


1 


7.11 


4.32 


2 


7.42 


4.37 


3 


7.89 


5.32 


4 


5.84 


5.79 


10 


3 


5Ac 


19 


1 


5.79 


2.26 


2 


5.47 


4.63 


3 


6.89 


4.53 


4 


6.16 


4.32 


1 


177 


5B1 


38 


4 


11.42 


2.76 




10.92 


3.18 


2 


11.76 


1.87 


3 


11.66 


2.84 


2 


27 


5A1 


43 


4 


10.30 


3.33 




8.35 


3.12 


2 


9.47 


4.07 


3 


8.84 


4.79 


3 


27 


5A2 


31 


4 


10.10 


3.90 




9.61 


3.00 


2 


9.74 


3.90 


3 


9.52 


4.90 


4 


83 


5A3 


38 


4 


6.76 


2.87 


1 


5.82 


2.39 


2 


6.13 


3.32 


3 


7.18 


3.68 


5 


83[5A4 


26 


4 


6.92 


3.88 




5.15 


3.08 


2 


5.77 


3.92 


3 


6.42 


4.96 


6 


835B3 


28 


4 


7.46 


3.04 




6.14 


3.07 


2 


7.11 


3.04 


3 


7.07 


3.54 


7 


83 5B4 


27 


4 


7.04 


3.96 




5.85 


3.78 


2 


7.26 


3.33 


3 


6.93 


4.15 


8 


3 


5Ba 


29 


4 


8.59 


3.48 


J 


7.48 


3.72 


2 


8.28 


3.83 


3 


8.07 


4.07 


9 


3 


5Bb 


23 


4 


7.61 


4.65 




6.57 


4.78 


2 


7.30 


4.83 


3 


7.57 


4.48 


10 


3 


5Bc 


15 


4 


6.80 


4.33 




6.73 


4.27 


2 


6.13 


5.53 


3 


6.53 


5.27 


1 


177 


5Ea 


40 


3 


11.92 


2.42 


4 


11.52 


2.92 




9.20 


3.20 


2 


10.37 


3.02 


2 


27 


4B2 


32 


3 


8.59 


3.72 


4 


7.16 


4.91 




6.12 


4.34 


2 


7.84 


4.06 


3 


27 


4B3 


27 


3 


8.74 


4.30 


4 


8.07 


5.37 




6.67 


4.44 


2 


7.70 


4.37 


4 


83 


5A5 


40 


3 


5.90 


4.20 


4 


6.67 


3.80 




5.67 


2.50 


2 


6.65 


3.07 


5 


83 


5A6 


29 


3 


7.79 


2.62 


4 


7.59 


3.31 




5.59 


2.45 


2 


7.00 


3.00 


6 


83 


5B5 


25 


3 


7.20 


2.80 


4 


6.80 


3.64 




5.16 


2.40 


2 


6.12 


3.60 


7 


83 


5B6 


27 


3 


7.48 


2.85 


4 


7.07 


3.44 




5.96 


3.19 


2 


6.67 


3.19 


8 


3 


6Aa 


30 


3 


10.77 


3.43 


4 


10.57 


3.47 




10.97 


2.40 


2 


10.63 


3.60 


9 


3 


6Ab 


34 


3 


9.71 


4.21 


4 


9.41 


4.00 




8.76 


4.24 


2 


9.29 


4.00 


10 


3 


6Ac 


24 


3 


8.21 


4.17 


4 


6.96 


5.29 




7.25 


3.92 


2 


7.00 


5.00 


1 


177 


5Eb 


31 


2 


11.45 


2.39 


3 


11.13 


3.23 


4 


11.32 


3.35 




10.74 


3.71 


2 


27 


4A2 


26 


2 


7.23 


3.27 


3 


7.62 


4.69 


4 


7.50 


4.58 




6.31 


3.42 


3 


27 


4A3 


25 


2 


6.12 


4.72 


3 


7.20 


3.96 


4 


6.04 


4.48 




5.32 


3.08 


4 


83 


5A7 


29 


2 


6.14 


2.93 


3 


6.86 


3.72 


4 


6.17 


4.03 




5.34 


2.79 


5 


83 


5A8 


29 


2 


6.17 


2.52 


3 


5.66 


3.41 


4 


5.66 


3.24 




5.34 


3.03 


6 


83 


5B7 


26 


2 


8.65 


2.65 


3 


8.12 


4.04 


4 


9.35 


3.27 




7.35 


3.15 


7 


83 


5B8 


21 


2 


8.33 


2.52 


3 


8.90 


3.05 


4 


8.24 


3.38 




7.05 


3.14 


8 


3 


6Ba 


28 


2 


9.39 


3.79 


3 


10.46 


3.50 


4 


9.64 


3.36 




10.25 


2.96 


9 


3 


6Bb 


25 


2 


8.24 


3.72 


3 


8.48 


4.52 


4 


9.72 


3.32 




8.04 


3.76 


10 


3 


6Bc 


21 


2 


8.95 


3.76 


3 


8.62 


4.48 


4 


8.48 


3.90 




8.43 


3.95 


1 40 i 


1,153 




8.16 


3.29 




7.84 


3.83 




7.89 


3.71 




7.79 


3.92 


Sum of 


righ1 


; ai 


ad 


















wrong . 






.. 11 


.45 




11.67 




1] 


1.60 




11.71 


Relative ai 


noun 


t'do 


ne 100 


.00 




101.92 




10] 


L.31 




102.27 


Per cent r 
Relative pe 


ght. 
r ceni 


;rig 


.. 71 
ht 100 


.27 
.00 




67.18 
94.26 




6i 
91 


?.02 
5.44 




66.52 
93.34 



24 



Studies of Mental Fatigue 



The following diagram illustrates these comparative per 
cents of increase in quantity (above the heavy horizontal line) 
and of decrease in quality (below the heavy horizontal line). 
The continuous lines represent the results by the detailed 
method of grading, and the dotted lines the results by the gross 
method of grading. 



I 



I 



§ ^ 



t^ 



I 



1 



Increase 



Quantity 



lOO.OO 




JOO.OO 



Decrease 

in 
Quality 



In these two series of per cents are apparently opposing 
results — a fairly continuous increase in quantity of work done 
at the four successive periods, with a very small increase in the 
second table at the third period ; and a fairly continuous 
decrease in quality, with a very small increase in the first 
table and a small increase in the second table at the third 
period. (These variations at the third period were due to the 
influence of the intermission from twelve to one o'clock. ) How- 
ever, this opposition may be more apparent than real. Fatigue 
often shows itself in a weakening of that inhibition which as- 
sures slower but more careful and consequently more correct 
work, the speed of the fatigued worker generally being a sign 
of decreased efficiency. (This result is evident in many 



Results 25 

different experiirients. ) But a claim that all the above- 
mentioned increase in quantity is due to fatigue would be a 
biased interpretation, though the influence of the noon inter- 
mission in arresting the increase at the third period and the 
presence of the greatest increase at the fourth period strengthen 
this claim. It is possible that some of the increase may be due 
to increased efficiency as the day advances, the children becom- 
ing more habituated to school work — having a greater "swing," 
as Offner says. The decrease in quality of work done at the 
four successive periods may more justly be considered as due 
almost entirely to fatigue, which is arrested by the noon inter- 
mission but is greatest at the fourth period. A slight boredom 
and consequent carelessness as the day advances may have 
affected the results in spite of my efforts to keep the interest 
nearly the same at all four periods. Altogether, we may con- 
sider that most, though not all, of this increase in quantity 
and decrease in quality is a sign of fatigue. 

It is impossible to combine accurately into one scries for 
each table the per cents of quantity and of quality at each of 
the four periods in order to make a single comparison of the 
work done. Any such combination, though arbitrary, ought 
to be based upon a just proportion of value between the two 
series. For instance, one per cent of increase in quantity 
should not cancel one per cent of decrease in quality because 
the latter per cent has more value than the former, more 
weight in- grading ability. A suggestive |)ro|)ortion is that 
based upon the per cents right of the sum of i-ight and wrong 
figures (or points) at the second, third, and fourth periods, 
these being in the first table 86.0G, 86. 17, and 85.46 per 
cent, respectively. These per cents give a ratio of value of 
1.00:. 8008 between the sum and the per cent right at the 
second period, a ratio of 1.00:. 8617 at the third period, and 
a ratio of 1.00:. 8546 at the fourth period. For the second 
period we multiply the 1.57 per cent in quantity by .8608 
and the 1.51 per cent in quality by 1.00, in order to reduce 
the per cents to equal value, and get 1.35 and 1.51 per cent, 
respectively. By subtracting the per cent of increase in 
quantity from the per cent of decrease in quality, we get a 
remaining decrease of .16 per cent. This gives 99.84 as the 
combined per cent of quantity and quality at the second period. 
In the same way we get 100.00 as the combined per cent at the 
third period and 99.80 at the fourth. The combined per cents 
in the second table are 95.55, 96.33, and 94.85 for the second, 



26 Studies of Mental Fatigue 

third, and fourth periods, respectively. It might be objected 
that, as both the increase in quantity and the decrease in quality 
are mainly due to fatigue, they should not be balanced against 
each other and only the remainder be subtracted from the 
100.00 per cent standard of the first period. One might even 
go so far as to suggest subtracting from this 100.00 per cent 
standard the sum of the per cents of increase and decrease. 
The reply is that the per cents of comparison must be based 
upon the actual work done, not upon an interpretation of the 
causes thereof, and that in grading such work an increase in 
quantity would naturally tend to offset a decrease in quality 
and vice versa, whether or not both the increase and the de- 
crease could be attributed to one cause. However, my sug- 
gested combination may show too little fatigue and is offered 
simply as an illustration of a possible method of reaching one 
series of per cents for purposes of comparison. 

The practice ejfect was calculated by rearranging the figures 
in the two total tables in columns according to tests rather than 
periods. As each test was given forty times — ten times at each 
of the four periods — the total result for each test combined the 
work at each of the four periods and thus neutralized the fatigue 
effect, which has often influenced the results in practice experi- 
ments. These total results were compared to find the practice 
effect. By the detailed method of grading, in quantity of work 
(sum of right and wrong figures) as compared with the first test, 
the ten groups together showed a respective increase of 8.91, 
14.09, and 13.67 per cent in the second, third, and fourth tests; 
in quality of work done (per cent of sum right) a respective de- 
crease of 1.35 and 1.31 per cent in the second and fourth tests, 
and an increase of 0.46 per cent in the third test. By the gross 
method of grading, in quantity of work done (sum of right 
and wrong points) as compared with the first test, the ten 
groups together showed a respective increase of 8.97, 15.39, 
and 13.97 per cent in the second, third, and fourth tests; and 
in quality of work done (per cent of sum right) a respective 
decrease of 2.00, 2.28, and 3.20 per cent in the second, third, 
and fourth tests. 



SECOND STUDY 

The tests were giA'en in February and March, 1913, to sixteen 
classes, 573 pupils, in three Lynchburg, Va., schools. The im- 
portant difference between this experiment and that in New 
York City is the amount of continuous work required by the 
tests. The New York classes were given four ten-minute tests 
at four periods of the school day, the Lynchburg classes two 
twenty-five minute tests at two periods.^ The subject matter 
used was the same in both experiments, but the Lynchburg 
classes took two tests as one. The reason for this extension of 
time was the supposition that a ten-minute spurt might not reveal 
the amount of fatigue present, the pupils working the short test 
with fairly unform efficiency at four periods of the school day. 
A continuous application for twenty-five minutes could hardly 
fail to reveal most of the fatigue present at the time of starting 
the test and the further possible fatigue from the longer test 
itself. If the fatigue from the test itself were equally present in 
the morning and in the afternoon work, it would be neutralized 
in the results ; but if it were greater in the afternoon on ac- 
count of greater fatigue at the time of starting, the difference 
would be evident in the results. The longer test, therefore, has 
two possibilities of revealing fatigue and is also a better illus- 
tration of the time required, though with less continuous pres- 
sure, for study and recitation in actual school practice. 

The Lynchburg tests were given on February 25 and 27, 
1913, to the 5A, 5B, 6A, and 6B classes in Biggers School; on 
February 26 and 28 to the 5A, 5B, 6A, and 6B classes in Mon- 
roe School; on March 11 and 13 to the 7B, 7 A, 6B, and 6A1 
classes in Federal School; on March 12 and 14 to the 6A2, 
5Bl, 5B2, and 5A classes in Federal School. The weather was 
mild, and window ventilation was used in addition to the fur- 
nace system. The schools had a one-session day, with a fifteen- 
minute recess soon after the morning tests and a twenty (some- 
times fifteen) minute recess before the afternoon tests. During 
the second recess many pupils ate lunch at home or school. 
This recess probably increased the efficiency in the afternoon 
tests ; but as every school has or should have a recess near this 
period of the school day, the conditions of the Lynchburg tests 
were typical, certainly for a one-session school day. The de- 

^As the Lynchburg classes were slower in this kind of work, twenty-five 
rather than twenty minutes were allowed. 



28 Studies of Meivtat. Fatigue 

partmental system of instruction allowed no uniform program 
of recitations and study periods in the classes tested. The chil- 
dren rei)resented for the most part hygienic opportunities at 
home and had ])een examined by their teachers for eyesight and 
hearing. All the classes included both boys and girls, the total 
being 2i)2 boys and 281 girls. The average age was 12.55 years. 

The following descri])tion is condensed and adapted from 
the First Study, to which the reader is referred for further 
discussion. The departmental teacher put aside her work for 
my test, but remained in the room at my request. I gave 
detailed directions to the class and then with the help of the 
teacher put on each desk a test pai)er with the blank side up. 
After the name, etc., had been written, the children turned the 
papers over immediately on signal and Avorked steadily for 
twenty-five minutes. Great care was taken to be exact in start- 
ing and stopping. The children thought they were being exam- 
ined for correctness and speed, but did not know how much time 
was being allowed and did not rush toward the end. The very 
few children who finished before the time was out looked over 
part of their papers. The spirit of the work was pleasant and 
earnest, and reduced to a minimum the element of boredom, 
probably the greatest influence in decreasing the quantity and 
quality of Avork in the ordinary routine of the school day. 

The time schedule was so arranged as to test each class in the 
morning and in the afternoon. The classes were combined into 
groTij's of two, one being a half-grade below (A) or above (B) 
the other. The first class in a group took the first test in the 
morning of the first day and the second test in the afternoon of 
the second day following; the second class took the first test in 
the afternoon of the first day and the second test in the morning 
of the second day after. In this way the practice effect of the 
first class in the second test in the afternoon was balanced 
against that of the second class in the morning and consequently 
neutralized, leaving the fatigue eft'ect free for comparison at the 
two periods. This arrangement was based upon a belief in the 
approximate equality of the ])ractice effect in the two classes in 
a group. Even the slight differences that might have occurred 
Avere neutralized by giA^ng the second test in the morning to the 
B classes and in the afternoon to the A classes of the first four 
groups, and then by giving the second test in the morning to the 
A classes and in the afternoon to the B classes of the second four 
groups.^ 



'One group was composed of 6A2 and 5B1, with the half-year relation- 
ship between classes as in the other groups but with different grades. 



Second Study 29 

Two groups were tested in a day, the two classes of the first 
group at about 9 :20 a. m. and 1 :30 p. m., respectively, and the 
two classes of the second group at about 9 :50 a. m. and 2 :00 
p. M.^ respectively. On the second day following, the classes 
tested before in the morniilg were tested in the afternoon, and 
vice versa; but the classes of the second group followed as be- 
fore immediately after the corresponding classes of the first 
group, each group constituting a complete unit by itself with 
the same time relationship between the classes as in all the other 
groups. Testing two groups a day gave a wider representation 
of the school day, fifty minutes of morning work and fifty min- 
utes of afternoon work. 

The papers were graded by me by a gross method of counting 
answers only, very similar to that used by Mr. Courtis. Each 
test contained thirty-two points divided as follows : Two groups 
of two examples were each credited with one point, this point 
being counted wrong on account of one or more mistakes in 
either example ; ten examples were each credited with one point, 
the point being counted wrong on account of one or more mis- 
takes in the example ; ten examples were each credited with two 
points, one point being counted wrong on account of one mis- 
take, and two points being counted wrong on account of two or 
more mistakes, in the example. A gross method of counting 
answers over-emphasizes mistakes in proportion to the total 
amount of work done, not only at one period but even in a com- 
parison between the percentage of error at two or more periods. 
The results of my New York tests showed that in the same 
papers the average increase in percentage of error at the three 
periods after the first period was by the gross method 3.2659 
times that by the detailed method of counting every figure put 
down by a child in working the examples. The increase in per- 
centage of error in the present results at the second period is, 
therefore, greater than the actual decrease in efficiency of the 
children tested. However, the gross method takes far less time 
for grading papers and is sufficiently accurate for comparison 
of the work at periods to which it has been uniformly applied. 



30 



Studies of Mental Fatigue 
Total Results. 





Class 


Pupils 


FIRST PEBIOD 


SECOND PERIOD 


School 


Test 


Right 


Wrong 


Test 


Right 


Wrong 


Biggers .. 
Monroe . . 
Federal . . 


5A 
5B 
6A 
6B 
5A 

6A 

6B 

7B 

7A 

6B 

6A1 

6A2 

5B1 

5B2 

5A 


43 
43 
44 
39 
34 
46 
35 
32 
33 
41 
30 
28 
33 
34 
28 
30 


1 

2 
1 
2 
1 
2 
1 
2 
1 
2 
1 
2 
1 
2 
1 
2 


12.67 
15.53 
15.61 
19.21 
14.09 
15.04 
17.17 
21.00 
19.64 
19.27 
15.60 
21.86 
14.61 
17.24 
12.64 
14.40 


5.02 
7.42 
7.34 
7.10 
6.44 
7.26 
4.54 
6.62 
5.00 
7.12 
5.27 
7.04 
5.33 
7.09 
5.96 
6.37 


2 
1 
2 
1 
2 
1 
2 
I 
2 
1 
2 
1 
2 
1 
2 
1 


16.53 
12.79 
16.64 
18.18 
15.15 
10.96 
20.14 
16.59 
21.33 
16.98 
17.83 
18.43 
17.09 
14.38 
15.96 
11.47 


6.14 
6.51 
9.23 
6.23 
8.56 
6.39 
6.54 
5.94 
7.12 
6.66 
6.80 
7.54 
6.58 
6.41 
7.18 
6.60 




16 


573 




16.60 


6.31 




16.28 


6.90 


Sum of right and wrong 
points 


22.91 

100.00 

72.46 


23.18 


Relative ai 
Per cent r 
Relative pe 


nount done. . 
ght 


101.18 
70.2.^ 


rcent right. . 




100. OC 






96.92 





The average of right and wrong points for the sixteen classes 
at each period were added and the general average taken, in 
which all individual, class, and group variations were merged. 
The Sinn of the general average of right and wrong points at the 
first period icas compared with that at the second period, giving 
an increase of 1.18 per cent ai the second period. The per cent 
right of the sum of right and wrong points at the first period 
ivas then compared with the per cent right at the second period, 
giving a decrease of 3.08 per cent at the second period. The in- 
crease in quantity was probably due in part to the same influ- 
ences as was the decrease in quality, gTeater speed and greater 
carelessness often going together. 

Even the slight decrease in efficiency shown by these results 
is larger than the actual decrease in the classes tested, because 



Second Study 31 

in Federal School the 5A class was somewhat disturbed in its 
afternoon work by the marching out of the other classes, and 
because the 7B and 6B classes had only a short indoor recess, 
on account of rain, before the afternoon tests. This is partly 
shown, though other influences may have entered, by the in- 
crease in quantity of 2.08 per cent and the decrease in quality 
of 3.37 per cent in the eight classes in Federal School, as com- 
pared with the increase in quantity of 0.22 per cent and the 
decrease in quality of 2.79 per cent in the eight classes in 
Biggers and Monroe Schools. 

As the average per cent of increase in quantity in the New 
York tests, for the three periods after the first period, was by 
the detailed method of grading 1.0164 times that by the gross 
method, we can surmise that the 1.18 per cent increase in quan- 
tity in the Lynchburg tests by the gross method would be about 
1.20 per cent by the detailed method. And as the average de- 
crease in quality in the New York tests was by the detailed 
method only 0.3062 times that by the gross method, we can sur- 
mise that the 3.08 per cent decrease in quality in the Lynch- 
burg tests would be about 0.94 per cent by the detailed method. 

By a comparison of the results by the gross method in the 
twenty-five minute test in the afternoon in Lynchburg with the 
average of the two ten-minute tests in the afternoon in New 
York, we have 1.18 per cent increase in quantity in Lynchburg 
as compared with 1.79 per cent, and 3.08 per cent decrease in 
quality as compared with 5.61 per cent. In spite of the longer 
requirement for continuous work, the Lynchburg children show 
a smaller decrease in efficiency, probably on account of their 
better hygienic opportunities at home. 

In order to determine whether the decrease in efficiency at 
the second period in Lynchburg was less in the more advanced 
grades, the following percentages were calculated : six fifth 
grades (three groups) showed an increase in quantity of 0.11 
per cent and a decrease in quality of 2.82 per cent; six sixth 
grades (three groups) showed an increase in quantity of 0.36 
per cent and a decrease in quality of 2.74 per cent; two seventh 
grades (one group) showed an increase in quantity of 2.08 per 
cent and a decrease in quality of 3.54 per cent. These slight 
differences seem to have no significance, the greater decrease 
in quality in the seventh grades being due mainly to the fact 
before mentioned that 7B had only a short indoor recess before 
the afternoon test. 



32 Studies of Mental Fatigue 

An important consideration is the greater decrease in eflB- 
ciency shown by the boys than by the girls, this difference even 
being noticeable in the greater restlessness of the boys during 
the tests. Complete tables of the sixteen class averages were 
made of the results by the boys and the girls, and the general 
averages, percentages, etc., were calculated. The boys showed 
an increase in quantity of 0.74 per cent and a decrease in qual- 
ity of 4.25 per cent ; the girls showed an increase in quantity 
of 1.62 per cent and a decrease in quality of 1.96 per cent. The 
boys showed an increase in quantity 0.4568 times that by the 
girls and a decrease in quality 2.1684 times that by the girls. 

The practice effect was calculated by rearranging the class 
averages in columns according to tests rather than periods, thus 
neutralizing for the most part the decrease in efficiency at the 
second period. The sixteen classes showed an increase in quan- 
tity of 13.22 per cent in the second test and a decrease in qual- 
ity of 0.50 per cent. 



THIRD STUDY 

The tests were given in December, 1914, to sixteen classes, 
476 pupils, in the Intermediate School in Roanoke, Va. In 
this experiment reasoning problems in arithmetic were used in 
place of the four fundamental operations in the liew York and 
Lynchburg experiments. Although the continued alertness re- 
quired of grammar-grade pupils in rapid computation may well 
be considered indicative of hygienic efficiency for other school 
work, it must be admitted that the four fundamental operations 
may become partially automatic in well-drilled children, and, 
therefore, be less affected by fatigue. Furthermore, reasoning 
problems were used in the third experiment as involving pro- 
cesses and effort more generally needed in meeting school re- 
quirements. 

In order to carry out in the third experiment the methods of 
the other two, it was necessary to use two reasoning tests that 
could be graded accurately and would be approximately equal 
in difficulty. The tests selected were Forms 1 and 3 of the 
Courtis Standard Test 'No. 8, since Mr. Courtis had proved by 
his very wide experience that these tests were as nearly equal as 
any so far made. They were given and scored according to the 
Courtis method, the number of examples done and the number 
right being calculated from the figures in the "Answer" column. 
The non-measureable elements in this gross method were mainly 
neutralized in the comparison of morning and afternoon work. 

On Monday, December 8, Form 2 of Test No. 8 was given 
as a preliminary test to all sixteen classes in order to acquaint 
them with the matter and method of the succeeding tests ; but 
the papers were not scored. By trying ten, fifteen, and twelve 
minutes as the time limit for this preliminary test, the twelve- 
minute limit was found to be most suitable for the classes con- 
cerned. For the succeeding tests the classes were divided into 
groups of four, each group containing a 7A, a 7B, a 6A, and a 
6B class of equal rank with other classes of the same half-grade. 
As the classes in a group were tested in rapid succession, about 
sixty-five minutes were required for a group — from 9 :25 to 
10 :30 in the morning or from 12 :50 to 1 :55 in the afternoon. 
The first test was given to Group 1 on Tuesday morning, to 
Group 2 on Tuesday afternoon, to Group 3 on Wednesday 
morning, and to Group 4 on Wednesday afternoon. The second 
test was given to Group 2 on Thursday morning, to Group 1 on 
Thursday afternoon, to Group 4 on Friday morning, and to 



34 Studies of Mental Fatigue 

Group 3 on Friday afternoon. Thus each class was tested in 
the morning and in the afternoon ; and each test was g•i^■on in 
the morning and in the afternoon to the same number of classes 
of relatively equal rank. By this method the practice effect in 
the second test was neutralized by approximately equal repre- 
sentation in the morning and in the afternoon results. To com- 
plete this neutralization the classes in Groups 1 and 2 were 
tested in descending order (7A, 7B, 6 A, 6B), and the classes in 
Groups 3 and 4 were tested in ascending order (6B, 6 A, 7B, 
7A). 

A teacher generally remained in the room during a test, but 
assisted me only in distributing and collecting the papers. The 
children enjoyed the tests, which they thought were only for 
correctness and speed. They did not know the time limit for 
the work ; and the few" that finished early spent the extra time 
in looking over their papers. Where children were absent from 
one test or where they did not follow important directions, their 
papers were thrown out. 

The hygienic conditions in the new school building were un- 
usually good, but there had been no medical inspection of the 
children. Opening exercises were held in each room from :00 
to 9 :20, recess was given from 12 :15 to 12 :35, and the first bell 
for dismissal was rung at 2:15. The only recess did not give 
much invigoration, because the boys' playgroimd was small and 
most girls remained indoors in spite of beautiful weather. 
Some pupils ate a light lunch at recess, but nearly all had din- 
ner at home after school. The departmental system of instruc- 
tion prevailed throughout with half-hour recitation periods. 
All classes included both boys and girls, the total represented in 
my results being 212 boys and 255 girls. The average age was 
14.18 years. 

After the papers were scored, the averages of the number of 
examples done and the number right in the morning and in the 
afternoon tests were made for each class. Then general aver- 
ages were made for the sixteen classes combined, and the morn- 
ing and the afternoon results were compared. The number of 
examples done in the afternoon was 0.68 per cent greater than 
in the morning; the per cent of examples right in the afternoon 
was 3.22 per cent less than in the morning. These per cents are 
strikingly similar to those from the Lynchburg and New York 
(average of two afternoon tests) experiments, where the in- 
crease in quantity in the afternoon was 1.18 and 1.79 per cent, 
respectively, and the decrease in quality 3.08 and 5.61 per cent, 



Third Study 



35 



respectively. As was shown by the New York results, the de- 
crease in quality would be less by a detailed method of grading. 

Total Results. 









MORNING 






AFTERNOON 


Class 


Pupils 


Test 


Examples 


Right 


Test 


Examples 


Right 


7A1 


26 


1 


5.96 


4.50 


2 


6.73 


5.27 


7B1 


30 


1 


5.60 


4.20 


2 


5.97 


4.77 


6A1 


31 


1 


4.87 


3.81 


2 


5.45 


4.23 


6B1 


29 


1 


4.83 


3.76 


2 


5.07 


3.97 


7A2 


32 


2 


6.84 


5.44 


1 


5.78 


4.00 


7B2 


35 


2 


6.23 


5.09 


1 


5.97 


4.31 


6A2 


27 


2 


6.37 


4.81 


1 


5.93 


4.19 


6B2 


25 


2 


5.88 


4.56 


1 


4.96 


3.00 


6B3 


24 


1 


4.96 


2.71 


2 


5.33 


3.58 


6A3 


26 


1 


5.04 


3.27 


2 


6.42 


4.19 


7B3 


35 


1 


4.74 


3.34 


2 


6.06 


4.51 


7A3 


33 


1 


6.64 


4.70 


2 


7.48 


5.27 


6B4 


28 


2 


6.00 


4.43 


1 


5.39 


3.54 


6A4 


29 


2 


5.79 


3.83 


1 


5.10 


3.31 


7B4 


28 


2 


6.82 


4.93 


1 


5.96 


4.00 


7A4 


29 


2 


7.00 


5.55 


1 


6.72 


5.14 


16 


467 




5.85 


4.31 




5.89 


4.20 


Relative nu 


mber 














done 






100.00 
73.68 






100.68 
71.31 




Per cent rig 


ht.... 




Relative per 


cent 














right 






100.00 






96.78 









The practice effect was calculated by rearranging the class 
averages according to first or second test rather than according 
to morning and afternoon, thus neutralizing for the most part 
the decrease in efficiency in the afternoon. The sixteen classes 
showed in the second test an average increase of 12.43 per cent 
in quantity and an average increase of 7.16 per cent in quality. 
This large practice effect was mainly due to the difficulty the 
children had at first in disregarding unnecessary figures in some 
of the examples. 

The seventh grade showed more relative efficiency in the aft- 
ernoon than did the sixth grade, probably on account of better 
discipline in the former. The seventh grade had an increase of 
1.61 per cent in quantity in the afternoon and a decrease of 2.82 
per cent in quality ; the sixth grade had a decrease of 0.04 per 
cent in quantity and a decrease of 3.67 per cent in quality. 



36 Studies of Mental Fatigue 

Complete tables of class and general averages were made for 
the girls and for the boys, showing the greater relative efficiency 
of the former in the afternoon. The girls had an increase of 
1.78 per cent in quantity in the afternoon and a decrease of 2.48 
per cent in quality; the boys a decrease of 1.30 per cent in 
quantity and a decrease of 3.76 per cent in quality. These 
significant results are similar to those from the Lynchburg tests. 



CONCLUSIONS 

The most important features of these experiments were the 
giving (a) of actual school tests (b) under actual school condi- 
tions (c) by the same examiner with the same methods (d) to a 
large number of classes and pupils. Every possible effort was 
made to get the work and attitude of the routine school day and 
to eliminate individual and group variations. The comparison 
of morning and afternoon results probably neutralized the effect 
of two differences from routine conditions : the tests were given 
by an outsider and offered a break in the regular school re- 
quirements. 

The per cent of increase in quantity and of decrease in qual- 
ity in the afternoon results, as compared with the morning re- 
sults, by the gross method of grading, may be summarized as 
follows : 



I i Increase in 'Decrease in 

City Classes j Pupils , Quantity I Quality 



New York' ! 40 1,153 I 1.79 I 5.61 

Lynchburg j 16 ! 573 ' 1.18 3.08 

Roanoke 16 476 i 0.68 3.22 



32 2,202 1.22 I 3.97 



Seventy-two classes, 2,202 children, in three cities, showed in 
the afternoon results an average increase in quantity of 1.22 per 
cent and an average decrease in quality of 3.97 per cent. 

The following tentative conclusions seem justified for gram- 
mar-grade pupils :- 

1. Mental fatigue in relation to the daily school program is 
far less than is generally believed, even if the tendency to do a 
greater amount of work with a greater per cent of error can be 
partly attributed to fatigue. 

'The averages of the t\vo afteraoon tests in New York are compared with 
the first morning test, as the second morning test did not represent the 
time or freshness of tlie morning test in Lynchburg and Roanoke, and the 
results were even below the afternoon average. 

'These conclusions will probably not apply to primary grades (to most 
children under eleven years of age), without modification as to length of 
daily school program, etc. 



''^ '*v VS k Ai ^ 




38 Studies of Mental Fatigue 

2. The opinion regarding the graduated advantages of suc- 
cessive periods of the school day, and the sentiment in favor of 
putting arithmetic and other supposedly difficult subjects near 
the opening of the morning and afternoon sessions, with an em- 
phasis upon the morning session, have not a sufficiently proved 
basis. 

3. The decrease in quality of work by pupils as the day ad- 
vances, considered to be more or less general in schools, is 
mainly due (a) to improper ventilation, lighting, heating, seat- 
ing, etc., (b) to physical defects in the children, and (c) to loss 
of interest by pupil and teacher in the monotonous school 
routine. 

4. With sound bodies, a hygienic school, proper classifica- 
tion, a vital and varied curriculum, and live teachers, most 
grammar-grade pui)ils will present no problem of fatigue in re- 
lation to the daily school program. 



VITA. 

William Harky Heck: Born Raleigh, N. C, 1879; B. A., 
Wake Forest College, N. C, 1897; Assistant Principal, Raleigh 
Male Academy, 1897-98; M. A., Wake Forest College, 1899; 
Graduate Student, Columbia University, 1899-1902 ; Univer- 
sity Fellow, 1900-01; Honorary Fellow, 1901-02; Assistant 
Secretary, General Education Board, 1902-05 ; Professor of 
Education, University of Virginia, 1905 — ; Graduate Student, 
Columbia University, 1911-12. 



,»v- 




